CN111564151B - A narrow-band active noise reduction optimization system for in-vehicle engine order noise - Google Patents

Abstract

The invention discloses a narrow-band active noise reduction optimization system for the order noise of an engine in a vehicle, which is used for smoothing an obtained rotating speed signal through an exponential smoothing formula aiming at the condition that the rotating speed of the engine fluctuates in the actual running process of the vehicle, constructing a more stable internal reference signal by using the smoothed rotating speed signal, obtaining an output signal of the narrow-band active noise reduction system according to the internal reference signal, and then updating the weight coefficient of a filter so as to continuously update the output signal. The system can solve the problem that the noise reduction performance of the system is reduced due to the fact that the internal reference signal presents obvious unsteady state characteristics caused by the fluctuation of the rotating speed of the engine in the actual situation, and has the potential of popularization and application in the field of active noise reduction in the vehicle.

Description

A narrow-band active noise reduction optimization system for in-vehicle engine order noise

technical field

The invention relates to the technical field of in-vehicle active noise control, and more particularly, the invention relates to a narrow-band active noise reduction optimization system for in-vehicle engine order noise.

Background technique

Traditionally, the passive control of noise mainly reduces noise by three methods: controlling the noise source, cutting off the propagation path, and protecting the receiver. For low-frequency noise with longer wavelengths, in order to achieve a good noise reduction effect, heavier materials are required, that is, higher costs. Active Noise Control (ANC) technology uses the principle of sound wave interference to achieve noise reduction by rationally arranging microphones and secondary sound sources in the scene. It is an efficient and cost-effective noise control method to effectively suppress the noise level of the object under the condition of the weight of the object, thereby improving the sound quality of the overall environment.

The current research on in-vehicle ANC systems mainly focuses on two technologies, Engine Order Cancellation (EOC) and Road Noise Cancellation (RNC). Among them, the engine order noise is usually controlled by a narrowband active noise reduction (Narrowband ANC, NANC) system based on the Filter-x Least Mean Square (FxLMS) algorithm to achieve selective control of the order noise. The rotational speed signal is obtained by the rotational speed sensor, and then the internal reference signal is constructed for the narrow-band active noise reduction system through the relationship between the frequency of the order noise and the rotational speed. However, in practice, the working state of the engine is not absolutely stable. Even if the vehicle runs at a relatively stable and constant speed, the engine speed still fluctuates within a certain range, which will cause the constructed internal reference signal to have obvious non-steady-state characteristics. , which reduces the convergence performance and noise reduction effect of the algorithm. Exponential smoothing (ES) happens to be mainly used for smoothing or forecasting time series. The principle is that the exponential smoothing value of any period is the weighted average of the actual observation value of the current period and the exponential smoothing value of the previous period. If the method can be applied to smooth the engine speed signal in the narrow-band active noise reduction system that reduces engine order noise, it will help to construct a more stable internal reference signal, thereby improving the performance of the system and promoting practical applications.

SUMMARY OF THE INVENTION

The purpose of the present invention is to design and develop a narrow-band active noise reduction optimization system for in-vehicle engine order noise. In view of the fluctuation of the engine speed, the obtained speed signal is smoothed by the exponential smoothing formula, and the smoothed speed signal is used to smooth the obtained speed signal. To construct a more stable internal reference signal, obtain the output signal of the narrowband active noise reduction system according to the internal reference signal, and then update the weight coefficient of the filter to update the output signal, thereby improving the convergence performance and reduction of the narrowband active noise reduction algorithm. noise performance.

The technical scheme provided by the present invention is:

A narrow-band active noise reduction optimization system for in-vehicle engine order noise, comprising the following steps:

Step 1. Obtain the engine speed signal;

Step 2: Convert the engine speed signal into a smooth speed signal:

R(t)=λ·R(t-1)+(1-λ)·r(t);

In the formula, R(t) is the smooth speed signal, t is the time index, and t=1, 2, 3...n, λ is the smoothing index, and the value range of λ is [0.9, 1), r(t) is the speed signal;

Step 3: Obtain the frequency of the engine order noise, the first internal reference signal and the second internal reference signal according to the smoothed rotational speed signal, thereby obtaining the speaker output signal of the narrowband active noise reduction optimization system:

为第t时刻的滤波器第一权值系数，

为第t时刻的滤波器第二权值系数，x_ai(t)为第一内部参考信号，x_bi(t)为第二内部参考信号。In the formula, y _N (t) is the output signal at time t, i is the target order, and i=1, 2, 3...q, q is the total number of angular frequencies of the target narrowband components,

is the first weight coefficient of the filter at time t,

is the second weight coefficient of the filter at time t, x _ai (t) is the first internal reference signal, and x _bi (t) is the second internal reference signal.

Preferably, the frequency of the engine order noise satisfies:

ω _i =2πR(t)η _i /60;

In the formula, ω _i is the angular frequency corresponding to the i-th target order component in the system reference noise signal, and η _i is the harmonic number corresponding to the i-th order component.

Preferably, the first internal reference signal satisfies:

x _ai (t)=cos(ω _i t);

In the formula, x _ai (t) is the first internal reference signal, ω _i is the angular frequency corresponding to the i-th target order component in the system reference noise signal, t is the time index, and t=1, 2, 3...n .

Preferably, the second internal reference signal satisfies:

x _bi (t)=sin(ω _i t);

In the formula, x _bi (t) is the second internal reference signal.

Preferably, the first weight coefficient of the filter can be adaptively updated as:

为第t时刻的滤波器第一权值系数，

为第t+1时刻的滤波器第一权值系数，μ_N为窄带主动降噪算法的滤波器的权值更新步长，

为第一内部参考信号经估计的次级通路滤波后得到的滤波信号，e_N(t)为残余噪声。In the formula,

is the first weight coefficient of the filter at time t,

is the first weight coefficient of the filter at time t+1, μ _N is the weight update step size of the filter of the narrowband active noise reduction algorithm,

is the filtered signal obtained after the first internal reference signal is filtered by the estimated secondary path, and e _N (t) is the residual noise.

Preferably, the second weight coefficient of the filter can be adaptively updated as:

为第t时刻的滤波器第二权值系数，

为第t+1次时刻的滤波器第二权值系数，

为第二内部参考信号经估计的次级通路滤波后得到的滤波信号。In the formula,

is the second weight coefficient of the filter at time t,

is the second weight coefficient of the filter at time t+1,

is a filtered signal obtained by filtering the estimated secondary path for the second internal reference signal.

Preferably, the filtered signal obtained after the first internal reference signal is filtered by the estimated secondary path satisfies:

为次级通路传递函数的估计的脉冲响应。In the formula,

is the estimated impulse response of the transfer function of the secondary path.

为次级通路传递函数的估计的脉冲响应。In the formula,

is the estimated impulse response of the transfer function of the secondary path.

Preferably, the residual noise satisfies:

e _N (t)=d _N (t)-y′ _N (t);

In the formula, d _N (t) is the primary desired signal, and y′ _N (t) is the secondary cancellation signal of the output signal at the t-th time passing through the secondary path.

Preferably, it also includes:

an exponential smoothing module, which is used to perform exponential smoothing processing on the collected rotational speed signal, and use the obtained result to construct the first internal reference signal and the second internal reference signal;

Two weight update modules, which are used to update the first weight coefficient and the second weight coefficient of the filter in real time;

a prediction filter module, which is used for receiving the result of the two-weight updating module and calculating the output signal;

An error synthesis module for summing the inverses of the primary desired signal and the secondary cancellation signal, and the error synthesis module can transmit the obtained result to the two-weight updating module.

The beneficial effects of the present invention:

Compared with the traditional narrow-band active noise reduction system used in the vehicle, the narrow-band active noise reduction optimization system designed and developed by the invention has the advantage of only passing a smooth formula with a small amount of calculation. , it can significantly improve the convergence performance and noise reduction performance of the algorithm when the engine speed fluctuates, making the noise reduction effect in the car more superior.

Description of drawings

FIG. 1 is a schematic block diagram of a narrow-band active noise reduction optimization system for in-vehicle engine order noise according to the present invention.

FIG. 2 is a time-domain diagram of an in-vehicle noise reference signal collected under a constant speed operating condition with a vehicle speed of 30 km/h in the comparative test according to the present invention.

FIG. 3 is a graph of a synchronous rotational speed signal collected under a constant speed operating condition with a vehicle speed of 30 km/h in the comparative test according to the present invention.

FIG. 4 is a frequency domain diagram of an in-vehicle noise reference signal collected under a constant speed operating condition with a vehicle speed of 30 km/h in the comparative test according to the present invention.

FIG. 5 is a time-domain diagram of an in-vehicle noise reference signal collected under a constant speed operating condition with a vehicle speed of 60 km/h in the comparative test according to the present invention.

FIG. 6 is a graph of a synchronous rotational speed signal collected under a constant speed operating condition with a vehicle speed of 60 km/h in the comparative test according to the present invention.

FIG. 7 is a frequency domain diagram of an in-vehicle noise reference signal collected under a constant speed operating condition with a vehicle speed of 60 km/h in the comparative test according to the present invention.

FIG. 8 is a graph showing the amplitude-frequency response of the primary channel and the secondary channel used in the comparative test of the present invention.

FIG. 9 is a phase-frequency response curve diagram of the primary channel and the secondary channel used in the comparative test of the present invention.

FIG. 10 is a graph showing the smoothing effect of the speed signal collected by the exponential smoothing module of the optimized narrowband active noise reduction system in the comparative test according to the present invention on the speed signal collected under a constant speed operating condition with a vehicle speed of 30km/h.

FIG. 11 is a frequency domain noise reduction effect diagram of in-vehicle noise reduction collected under a constant speed operating condition with a vehicle speed of 30 km/h in the comparative test according to the present invention.

12 is a graph showing the smoothing effect of the speed signal collected by the exponential smoothing module of the optimized narrowband active noise reduction system in the comparative test of the present invention on the speed signal collected under a constant speed operating condition with a vehicle speed of 60 km/h.

FIG. 13 is a frequency domain noise reduction effect diagram of in-vehicle noise reduction collected under a constant speed operating condition with a vehicle speed of 60km/h in the comparative test according to the present invention.

FIG. 14 is a mean square value (MSE) curve diagram of the error signal of in-vehicle noise reduction collected under a constant speed operating condition with a vehicle speed of 30km/h in the comparative test according to the present invention.

FIG. 15 is a mean square value (MSE) curve diagram of the error signal of the noise reduction in the vehicle collected under the constant speed operating condition of the vehicle speed of 60km/h in the comparative test according to the present invention.

Detailed ways

The present invention will be further described in detail below, so that those skilled in the art can implement it with reference to the description.

As shown in FIG. 1 , a narrow-band active noise reduction optimization system for in-vehicle engine order noise provided by the present invention includes: an exponential smoothing module, a two-weight update module, a prediction filter module, and an error synthesis module. Wherein, the exponential smoothing module is used to perform exponential smoothing processing on the collected rotational speed signal, and the obtained results are used to construct the first internal reference signal and the second internal reference signal; the two weight updating module adopts adaptive iteration formula to update the prediction filter coefficients in real time, and transmit the result to the prediction filter module; the prediction filter module is used to calculate the output signal, and preferably, the prediction filter adopts a finite impulse response filter (FIR filter); the error synthesis module sums the inverses of the primary expected signal and the secondary cancellation signal, and transmits the result to the two-weight updating module.

是次级通路传递函数的估计，S(z)为次级通路传递函数，并且设定

次级通路传递函数代表现实存在的一种对声音信号的影响，它是客观存在，不需要获取，而次级通路传递函数的估计可以通过次级通路建模辨识来获得；d_N(t)是初级期望信号，也叫做初级噪声，即车内目标降噪区域的噪声，y_N(t)是降噪系统的输出信号，y′_N(t)是输出信号经过次级通路的次级抵消信号，e_N(t)是初级噪声与次级抵消信号在目标降噪区域叠加后的残余噪声信号，也叫做误差信号，用于反馈至二权值更新模块进行权值更新。As shown in Figure 1, the basic principle of the active noise control system is the superposition and cancellation of sound waves. There is an algorithm iterative calculation of the active noise reduction system, and a series of signals with the same phase and opposite phase as the target noise or the primary expected noise are emitted through the speaker. Among them, the transfer function of the channel between the speaker and the target noise reduction area is the secondary path transfer function, which represents the influence of the channel on the sound amplitude and phase;

is the estimate of the transfer function of the secondary path, S(z) is the transfer function of the secondary path, and set

The transfer function of the secondary path represents a real influence on the sound signal, it exists objectively and does not need to be acquired, and the estimation of the transfer function of the secondary path can be obtained through the identification of the secondary path modeling; d _N (t) is the primary desired signal, also called primary noise, that is, the noise in the target noise reduction area in the vehicle, y _N (t) is the output signal of the noise reduction system, and y′ _N (t) is the secondary cancellation of the output signal through the secondary path The signal, e _N (t) is the residual noise signal after the primary noise and the secondary cancellation signal are superimposed in the target noise reduction area, also called the error signal, which is used for feedback to the two weight update module for weight update.

为第一内部参考信号经估计的次级通路滤波后得到的滤波信号，

为第二内部参考信号经估计的次级通路滤波后得到的滤波信号。In the narrowband active noise reduction subsystem, x _ai (t) is the first internal reference signal of the subsystem, x _bi (t) is the second internal reference signal of the subsystem,

is the filtered signal obtained by filtering the estimated secondary path for the first internal reference signal,

is a filtered signal obtained by filtering the estimated secondary path for the second internal reference signal.

When performing active noise reduction for the engine order noise in the car, the noise reduction process is as follows:

First, perform exponential smoothing on the synchronization signal provided by the speed sensor, that is, the speed signal, to obtain a smooth speed signal:

R(t)=λ·R(t-1)+(1-λ)·r(t);

In the formula, R(t) is the smoothing speed signal, t is the time index, and t=1, 2, 3...n, λ is the smoothing index, which is a constant, and the value range of λ is [0.9, 1) , r(t) is the speed signal.

From this, the frequency of the target narrowband component, that is, the frequency of the engine order noise, is calculated as:

ω _i =2πR(n)i/60;

In the formula, ω _i is the angular frequency corresponding to the i-th target order component in the system reference noise signal, η _i is the harmonic number corresponding to the i-th order component, i is the target order, and i=1, 2 , 3...q, q is the total number of angular frequencies of the target narrowband component.

The narrowband active noise reduction subsystem synthesizes the first internal reference signal and the second internal reference signal accordingly, and the results are as follows:

x _ai (t)=cos(ω _i t);

x _bi (t)=sin(ω _i t);

In the formula, x _ai (t) is the first internal reference signal, and x _bi (t) is the second internal reference signal.

After the first internal reference signal and the second internal reference signal are filtered by the estimated secondary paths, respectively, the filtered signals are obtained, and the results are as follows:

为第一内部参考信号经估计的次级通路滤波后得到的滤波信号，

为第二内部参考信号经估计的次级通路滤波后得到的滤波信号，

为次级通路传递函数的估计的脉冲响应，s(t)为次级通道传递函数的脉冲响应。In the formula,

is the filtered signal obtained by filtering the estimated secondary path for the first internal reference signal,

is the filtered signal obtained by filtering the estimated secondary path for the second internal reference signal,

is the estimated impulse response of the transfer function of the secondary channel, and s(t) is the impulse response of the transfer function of the secondary channel.

The prediction filter module convolves the obtained first weight coefficient of the filter and the second weight coefficient of the filter with the first internal reference signal and the second internal reference signal respectively and sums them up as the subsystem output signal, which is expressed as follows:

为t时刻的滤波器第一权值系数，

为t时刻的滤波器第二权值系数，x_ai(t)为第一内部参考信号，x_bi(t)为第二内部参考信号。In the formula, y _N (t) is the output signal at time t, i is the target order, and i=1, 2, 3...q, q is the total number of angular frequencies of the target narrowband components,

is the first weight coefficient of the filter at time t,

is the second weight coefficient of the filter at time t, x _ai (t) is the first internal reference signal, and x _bi (t) is the second internal reference signal.

The error synthesis module sums the inverses of the primary desired signal and the secondary cancellation signal to obtain an error signal. The results are as follows:

e _N (t)=d _N (t)-y′ _N (t);

In the formula, d _N (t) is the primary desired signal, and y' _N (t) is the secondary cancellation signal of the t-th output signal passing through the secondary path.

The error signal and the filtered signal are brought into the adaptive iterative formula in the two-weight updating module to update the weights.

The adaptive iterative formula in the two-weight update module is based on the principle of steepest descent and is expressed as:

为第t时刻预测滤波器的第一权值系数，

为第t+1时刻预测滤波器的第一权值系数；

为第t时刻预测滤波器的第二权值系数，

为第t+1时刻预测滤波器的第二权值系数，μ_N为窄带主动降噪子系统的滤波器的权值更新步长，J_a(t)为自适应迭代公式的第一代价函数，J_b(t)为自适应迭代公式的第二代价函数，

为第一代价函数的梯度，

为第二代价函数的梯度。in,

is the first weight coefficient of the prediction filter at time t,

is the first weight coefficient of the prediction filter at time t+1;

is the second weight coefficient of the prediction filter at time t,

is the second weight coefficient of the prediction filter at time t+1, μ _N is the weight update step size of the filter of the narrowband active noise reduction subsystem, and J _a (t) is the first cost function of the adaptive iterative formula , J _b (t) is the second cost function of the adaptive iteration formula,

is the gradient of the first cost function,

is the gradient of the second cost function.

And the first cost function and the second cost function satisfy:

J _a (t)=J _b (t)=E[e _N ² (t)];

The gradient of the first cost function and the gradient of the second cost function are expressed as follows:

Among them, e _N (t) is the error signal, that is, the output signal of the error synthesis sub-module.

The update results of the first weight coefficient and the second weight coefficient of the prediction filter can be obtained as follows:

By repeating the above process continuously, the effective control of the engine order noise in the target scene can be achieved.

In order to test the noise reduction performance of the system proposed in the present invention for the order noise of the in-vehicle engine, the optimized narrow-band active noise reduction system for the in-vehicle engine order noise provided in the present invention is compared with the traditional narrow-band active noise reduction in the prior art. The system is compared and tested as follows:

As shown in Figure 2-4, the test results of in-vehicle noise and synchronous speed signal under the constant speed condition of the vehicle speed of 30km/h, as shown in Figure 5-7, under the constant speed condition of the vehicle speed of 60km/h And the test results of the synchronous speed signal, among which, Figure 2 and Figure 5 are the in-vehicle noise signals collected under the two operating conditions of 30km/h and 60km/h, and Figure 3 and Figure 6 are the corresponding data collected under the two operating conditions. Synchronous speed signal, Figure 4 and Figure 7 are the spectrum diagrams of the in-vehicle noise signals collected under two operating conditions.

In the experiment, P(z) is the transfer function of the primary path, S(z) is the transfer function of the secondary path, both of which are represented by an FIR filter with an order of 64. The frequency responses of the two paths are shown in Figures 8 and 8. As shown in FIG. 9 , wherein, FIG. 8 is the amplitude-frequency response curve of the two channels, and FIG. 9 is the phase-frequency response curve of the two channels.

The filters involved in the two-weight update module and the prediction filter module in the system provided by the present invention are all FIR filters with an order of 1. Among them, the step size parameter in the two-weight update module is μ _N =9.6×10 ⁻⁴ under the working condition of the vehicle speed of 30km/h, and the corresponding step size under the working condition of 60km/h is μ _N =1.6× 10 ^-3 , the target narrow-band component frequency of system noise reduction corresponds to the first and second orders of engine order noise, ie η ₁ =1, η ₂ =2.

As shown in Figure 10-13, it can be seen from the frequency domain that the traditional narrowband active noise reduction system is not very ideal for the control of engine order noise in real vehicles, and the frequency band near the target narrowband component frequency even shows sound pressure. The phenomenon of level rise, the noise reduction performance is not good. In contrast, the system proposed in the present invention has a superior noise reduction effect on the suppression of engine order noise, and does not cause an increase in the noise sound pressure level of the nearby frequency band.

According to the calculation, the traditional active narrowband active noise reduction system can achieve a total noise reduction of 0.62dB and 0.86dB respectively under two uniform speed conditions of 30km/h and 60km/h, while the system proposed in the present invention can achieve a total noise reduction of 0.62dB and 0.86dB respectively under the two working conditions. It can achieve a total noise reduction of 1.77dB and 1.40dB, with more prominent noise reduction performance.

In addition, as shown in Figure 14 and Figure 15, which are the mean square value curves of the error signals of the two systems, it can be seen that the performance of the two systems in terms of steady-state error in the convergence performance and their noise reduction ability in the frequency domain Basically the same, and the system proposed in the present invention exhibits better stability.

Compared with the traditional narrow-band active noise reduction system used in the vehicle, the narrow-band active noise reduction optimization system designed and developed by the present invention has the advantage that only a smooth formula with a small amount of calculation is used, and the It can significantly improve the convergence performance and noise reduction performance of the algorithm when the engine speed fluctuates. Specifically, the obtained speed signal is smoothed by the exponential smoothing formula, and the smoothed speed signal is used to construct a more stable internal reference signal. , obtain the output signal of the narrowband active noise reduction system according to the internal reference signal, and then update the weight coefficient of the filter to update the output signal, so that the noise reduction performance in the vehicle is better.

Although the embodiment of the present invention has been disclosed as above, it is not limited to the application listed in the description and the embodiment, and it can be applied to various fields suitable for the present invention. For those skilled in the art, it can be easily Therefore, the invention is not limited to the specific details and embodiments shown and described herein without departing from the general concept defined by the appended claims and the scope of equivalents.

Claims (4)

1. A narrow-band active noise reduction optimization system for the order noise of an engine in a vehicle is characterized by comprising the following steps:

step one, obtaining an engine rotating speed signal;

step two, converting the engine rotating speed signal into a smooth rotating speed signal:

R(t)＝λ·R(t-1)+(1-λ)·r(t)；

wherein, r (t) is a smooth rotation speed signal, t is a time index, t is 1, 2, 3 … n, λ is a smooth index, λ has a value range of [0.9, 1 ], and r (t) is a rotation speed signal;

step three, obtaining the frequency of the engine order noise, the first internal reference signal and the second internal reference signal according to the smooth rotating speed signal:

ω _i ＝2πR(t)η _i /60；

x _ai (t)＝cos(ω _i t)；

x _bi (t)＝sin(ω _i t)；

in the formula, omega _i For the angular frequency, eta, corresponding to the ith target order component in the system reference noise signal _i Harmonic number, x, corresponding to the ith order component _ai (t) is the first internal reference signal, x _bi (t) is a second internal reference signal;

the loudspeaker output signal of the narrow-band active noise reduction optimization system is obtained by the following steps:

in the formula, y _N (t) is the output signal at time t, i is the target order number, and i is 1, 2, 3 … q, q is the total number of angular frequencies of the target narrow-band component,

the first weight coefficients of the filter at the t-th time,

is the second weight coefficient, x, of the filter at the t-th moment _ai (t) is the first internal reference signal, x _bi (t) is a second internal reference signal;

wherein, the first weight coefficient of the filter can be adaptively updated as:

in the formula,

the first weight coefficients of the filter at the t-th time,

is the first weight coefficient, mu, of the filter at the t +1 th moment _N Is a narrow bandThe weight update step size of the filter of the active noise reduction algorithm,

a filtered signal obtained by filtering the estimated secondary path of the first internal reference signal, e _N (t) is residual noise;

the second weight coefficient of the filter can be adaptively updated as follows:

in the formula,

the second weight coefficients of the filter at the t-th time,

the second weight coefficients of the filter at the t +1 th time,

filtering the second internal reference signal by the estimated secondary path to obtain a filtered signal;

wherein, the narrowband of engine order noise in the car initiative noise reduction optimizing system includes:

an exponential smoothing module, configured to perform exponential smoothing on the collected engine speed signal, and use an obtained result to construct the first internal reference signal and the second internal reference signal;

the two weight updating modules are used for updating the first weight coefficient and the second weight coefficient of the filter in real time;

a prediction filter module for receiving the results of the two weight update modules and calculating output signals;

an error synthesis module for summing the inverses of the primary desired signal and the secondary cancellation signal, and the error synthesis module can transmit the result to the two weight update module.

2. The system for narrowband active noise reduction optimization of an in-vehicle engine order noise of claim 1, wherein the first internal reference signal is filtered by the estimated secondary path to obtain a filtered signal satisfying:

in the formula,

an estimated impulse response of the secondary path transfer function.

3. The system for narrowband active noise reduction optimization of an in-vehicle engine order noise of claim 2, wherein the second internal reference signal is filtered by the estimated secondary path to obtain a filtered signal satisfying:

in the formula,

an estimated impulse response of the secondary path transfer function.

4. The in-vehicle engine order noise narrowband active noise reduction optimization system of claim 3, wherein the residual noise satisfies:

e _N (t)＝d _N (t)-y′ _N (t)；

in the formula (d) _N (t) is the primary desired signal, y' _N And (t) is a secondary cancellation signal of the output signal at the t-th time point through the secondary path.

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